Dynamic free-surface deformations in axisymmetric liquid bridges

Thermocapillary convection in a differentially heated liquid bridge is investigated in a two-dimensional numerical study. The deformable free surface is obtained as a solution of the coupled transport equations at fixed unit Prandtl number and aspect ratio. Only steady convection can be realized in this axisymmetric computation with either non-deformable or deformable surfaces. Dynamic free-surface deformations do not induce transitions to oscillatory convection even at large Reynolds numbers. Free surfaces are convex near the cold wall due to large surface pressures at the stagnation-point. Near the hot wall they change from concave to convex with increasing Re due to large normal viscous stresses. Large Capillary numbers cause additional surface ripples there while having little effect on the interior. Heat loss from the free surface has dramatic influence on the dynamics and must be included in theoretical models of thermocapillary instabilities.